Question

Two blocks with mass m1 = 7.6 kg and m2 = 8.1 kg are connected by a massless string over a frictionless and massless pulley. The angle of the incline is equal to 32.5°. The kinetic coefficient of friction between m1 and the incline is 0.11.

What is the minimum value of the static friction coefficient that will prevent m1 from starting to move if it is at rest.

Find the magnitude of the acceleration of the system if m1 is moving up the incline.

Find the magnitude of the acceleration of the system if m1 is moving down the incline.

Answer 1

a] Let tension be T,

T = m2g,

and T = m1g sin theta + um1g cos theta

m2g = m1g sin theta + um1g cos theta

8.1 = 7.6* sin 32.5 degree + u*7.6*cos 32.5 degree

u = 0.627

b] Now by force equations, m2g - T = m2a

T - m1g sin theta - um1g cos theta = m1a

adding them, m2g - m1g sin theta - um1g cos theta = (m1+m2)a

a = [m2g - m1g sin theta - um1g cos theta]/(m1+m2)

= (8.1*9.8-7.6*9.8*sin 32.5 degree-0.11*7.6*9.8*cos 32.5 degree)/(7.6+8.1)

= 2.067 m/s^2

c] Again by force equations, -m2g+T = m2a

-T + m1g sin theta - um1g cos theta = m1a

adding them, -m2g + m1g sin theta - um1g cos theta = (m1+m2)a

a = [-m2g + m1g sin theta - um1g cos theta]/(m1+m2)

= (-8.1*9.8+7.6*9.8*sin 32.5 degree-0.11*7.6*9.8*cos 32.5 degree)/(7.6+8.1)

= -2.95 m/s^2